Think of it like walking in a rainstorm. Walk at a slow pace and most of the rain hits your head, but if you're moving very fast all of the rain will seem to be coming from the front because you are running into it instead of it running into you.
If you travel very close to c (relative to everything else) then due to length contraction everything else in the universe is 0 metres away. Likewise time appears stopped on everything else moving close to c relative to you, due to time dilation. (Is this right? I've never thought of it this way before).
Blue shift (aka increased apparent frequency) is caused by the velocity between you and the source, not the velocity of the source. That is how the speed of light works in General Relativity. If you move toward a photon is doesn’t get faster, it gets higher frequency. If that’s in the visible range it shifts toward the blue end of the spectrum.
If you move fast enough, all of the ultraviolet light coming from behind you becomes visible light. A little faster and all of the ultraviolet light in front of you becomes X-rays. And all of the hard x-rays become gamma rays.
Even if the photon is coming from the side, just slightly ahead of you, you are ramming into it at near lightspeed. You can't add up speeds in newtonian way so energy goes (for you) into blueshift.
I don't understand that one, could you please expand on how it works ?